Question

the iq scores and science test scores of fourth grade students are given by the regression line ( hat{y} = -20.3 + 0.7499s ), where ( hat{y} ) is the predicted science score and ( s ) is the iq score. an actual science test score for a student is 52.6 with an iq of 100. find and interpret the residual.
-1.99, the regression line underpredicts the students science test score.
1.99, the regression line underpredicts the students science test score.
1.99, the regression line overpredicts the students science test score.
-1.99, the regression line overpredicts the students science test score.

Explanation:

Step1: Calculate predicted score

Substitute $s=100$ into $\hat{y}=-20.3+0.7409s$
$\hat{y}=-20.3+0.7409\times100 = -20.3+74.09 = 53.79$

Step2: Compute residual

Residual = Actual score - Predicted score
$\text{Residual}=52.6 - 53.79 = -1.19$

Step3: Interpret residual

A negative residual means the regression line overpredicts the actual score.

Answer:

-1.19; The regression line overpredicts the student's science test score.